Order of Operations Worksheets

In mathematics, the order of operations is the order in which factors in an equation are solved when more than one operations exist in the equation. The correct order of operations across the entire field is as follows: Parenthesis/Brackets, Exponents, Division, Multiplication, Addition, Subtraction.

Teachers hoping to educate young mathematicians on this principle should emphasize the importance of the sequence in which an equation is solved, but also make it fun and easy to remember the correct order of operations, which is why many teachers use the acronym PEMDAS along with the phrase "Please Excuse My Dear Aunt Sally" to help students remember the proper sequence.

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Worksheet #1

Electronics professor discussing equation on whiteboard to engineering students, one in wheelchair
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In the ​first order of operations worksheet (PDF), students are asked to solve problems which put their understanding of the rules and meaning of PEMDAS to the test. However, it's important to also remind students that the order of operations includes the following specifics:

  1. Calculations must be done from left to right.
  2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first.
  3. Exponents (or radicals) must be done next.
  4. Multiply and divide in the order the operations occur.
  5. Add and subtract in the order the operations occur.

Students should be encouraged to simply inside groupings of parentheses, brackets, and braces first, working from the innermost part first then moving outward and simplify all exponents. 

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Worksheet #2

Worksheet 2

 Deb Russell

The second order of operations worksheet (PDF) continues this focus on understanding the rules of the order of operations, but can be tricky for some students who are new to the subject. It is important for teachers to explain what would happen if the order of operations is not followed which could drastically impact the solution to the equation.

Take question three in the linked PDF worksheet—if the student were to add 5+7 before simplifying the exponent, they might try to simplify 12(or 1733), which is much higher than 7​3+5 (or 348) and the resulting outcome would be even higher than the correct answer of 348.

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Worksheet #3

Worksheet 3

 Deb Russell

Use this order of operations worksheet (PDF) to further test your students, which ventures into multiplication, addition, and exponentials all inside of parentheticals, which can further confuse students who might forget that the order of operations essentially resets within parentheticals and must then occur outside of them.

Look at question 12 in the linked printable worksheet—there are addition and multiplication operations that need to occur outside of the parenthesis and there are addition, division, and exponentials inside the parenthesis.

According to the order of operations, students would solve this equation by first resolving the parenthesis, which would begin with simplifying the exponential, then dividing it by 1 and adding 8 to that result. Finally, the student would multiply the solution to that by 3 then add 2 to get an answer of 401.

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Additional Worksheets

Worksheet

 Deb Russell

Use the fourthfifth, and sixth printable PDF worksheets to completely test your students on their comprehension of the order of operations. These challenge your class to use comprehension skills and deductive reasoning to determine how to properly solve these problems.

Many of the equations have multiple exponentials so it's important to allow your students plenty of time to complete these more complex math problems. Answers for these worksheets, like the rest linked on this page, are on the second page of each PDF document—make sure you don't hand them out to your students instead of the test!